Every person’s genetic instruction book is a trove of never-before-seen genetic variants, according to an ongoing effort to map human genetic diversity.

In recent years, scientists have discovered that humans carry far more rare genetic variants than anyone ever thought. Now, a major effort to map the diversity of humans’ genetic makeup — called the 1000 Genomes Project — has turned up even more variety than researchers had expected. The project has now lived up to its name, completing a co...